The application of a stress to the surface of a sample of material, or the relief of that stress, may cause deformation of the sample. Such deformation is elastic if it occurs simultaneously with the application or removal of the stress and is viscoelastic if the sample slowly deforms with time after the stress has been applied or removed. The deformation in many materials may not be uniform, especially when the stress is nonuniform. For example, the viscoelastic deformation of a core sample taken from a subterranean formation is nonuniform following its removal from the stress created by the anisotropic in-situ formation stress. The deformation of the core sample in a vertical plane through the sample will be different than the deformation in a horizontal plane through the sample and such deformations are further complicated by the directionally dependent elastic constants of the core sample material and by the directionally of horizontal stresses in the subterranean formation.
Measurement of this deformation has been carried out by strain gages or linear voltage displacement transducers (LVDTs) located at a plurality of discreet points on the surface of a sample of a material. For example, FIG. 1 illustrates a core sample 10 having a plurality of strain gages 11 affixed to its outer surface for measuring deformation at the affixed points, while FIG. 2 illustrates a core sample 13 having a plurality of LVDT's 14 affixed to its outer surface for measuring deformation. Consequently, only the deformation at such discrete points is being measured and assumption is made that deformation in a plane, horizontal or vertical, through each of such discrete points is uniform or elliptical.
However, because of directionally dependent elastic constants of the sample material and differential stresses on the sample material, such as directionally dependent stresses in subterranean formations, such assumptions as to uniform deformation in a horizontal or vertical plane will be invalid and any attempt to calculate deformation of the entire sample from such discrete measurements will fail. Accordingly, it is an object of the present invention to provide a measurement of the true stress deformation of the entire body of a sample material, viscoelastic, elastic or thermal, without making assumptions as to how the sample material should deform.